Linear.Quaternion:$cexp from linear-1.19.1.3

Percentage Accurate: 99.8% → 99.8%

Time: 7.3s

Alternatives: 6

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x \cdot \frac{\sin y}{y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x (/ (sin y) y)))

C

double code(double x, double y) {
	return x * (sin(y) / y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (sin(y) / y)
end function

Java

public static double code(double x, double y) {
	return x * (Math.sin(y) / y);
}

Python

def code(x, y):
	return x * (math.sin(y) / y)

Julia

function code(x, y)
	return Float64(x * Float64(sin(y) / y))
end

MATLAB

function tmp = code(x, y)
	tmp = x * (sin(y) / y);
end

Wolfram

code[x_, y_] := N[(x * N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{\sin y}{y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x (/ (sin y) y)))

C

double code(double x, double y) {
	return x * (sin(y) / y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (sin(y) / y)
end function

Java

public static double code(double x, double y) {
	return x * (Math.sin(y) / y);
}

Python

def code(x, y):
	return x * (math.sin(y) / y)

Julia

function code(x, y)
	return Float64(x * Float64(sin(y) / y))
end

MATLAB

function tmp = code(x, y)
	tmp = x * (sin(y) / y);
end

Wolfram

code[x_, y_] := N[(x * N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{\sin y}{y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x (/ (sin y) y)))

C

double code(double x, double y) {
	return x * (sin(y) / y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (sin(y) / y)
end function

Java

public static double code(double x, double y) {
	return x * (Math.sin(y) / y);
}

Python

def code(x, y):
	return x * (math.sin(y) / y)

Julia

function code(x, y)
	return Float64(x * Float64(sin(y) / y))
end

MATLAB

function tmp = code(x, y)
	tmp = x * (sin(y) / y);
end

Wolfram

code[x_, y_] := N[(x * N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[x \cdot \frac{\sin y}{y} \]

2. Final simplification 99.8%

   \[\leadsto x \cdot \frac{\sin y}{y} \]

Alternative 2: 57.5% accurate, 9.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.4:\\ \;\;\;\;x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{y}{x}}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 6.4)
   (* x (+ 1.0 (* -0.16666666666666666 (* y y))))
   (/ 1.0 (/ (/ y x) y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 6.4) {
		tmp = x * (1.0 + (-0.16666666666666666 * (y * y)));
	} else {
		tmp = 1.0 / ((y / x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 6.4d0) then
        tmp = x * (1.0d0 + ((-0.16666666666666666d0) * (y * y)))
    else
        tmp = 1.0d0 / ((y / x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 6.4) {
		tmp = x * (1.0 + (-0.16666666666666666 * (y * y)));
	} else {
		tmp = 1.0 / ((y / x) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 6.4:
		tmp = x * (1.0 + (-0.16666666666666666 * (y * y)))
	else:
		tmp = 1.0 / ((y / x) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 6.4)
		tmp = Float64(x * Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y))));
	else
		tmp = Float64(1.0 / Float64(Float64(y / x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 6.4)
		tmp = x * (1.0 + (-0.16666666666666666 * (y * y)));
	else
		tmp = 1.0 / ((y / x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 6.4], N[(x * N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(y / x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.4000000000000004

   1. Initial program 99.9%

      \[x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in y around 0 65.3%

      \[\leadsto x \cdot \color{blue}{\left(1 + -0.16666666666666666 \cdot {y}^{2}\right)} \]
   3. Step-by-step derivation

      1. unpow2 65.3%

         \[\leadsto x \cdot \left(1 + -0.16666666666666666 \cdot \color{blue}{\left(y \cdot y\right)}\right) \]

   4. Simplified 65.3%

      \[\leadsto x \cdot \color{blue}{\left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)} \]

   if 6.4000000000000004 < y

   1. Initial program 99.6%

      \[x \cdot \frac{\sin y}{y} \]
   2. Step-by-step derivation

      1. *-commutative 99.6%

         \[\leadsto \color{blue}{\frac{\sin y}{y} \cdot x} \]

      2. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{\sin y \cdot x}{y}} \]

      3. associate-*r/ 99.7%

         \[\leadsto \color{blue}{\sin y \cdot \frac{x}{y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\sin y \cdot \frac{x}{y}} \]

   4. Taylor expanded in y around 0 29.0%

      \[\leadsto \color{blue}{y} \cdot \frac{x}{y} \]
   5. Step-by-step derivation

      1. clear-num 30.7%

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{y}{x}}} \]

      2. un-div-inv 30.7%

         \[\leadsto \color{blue}{\frac{y}{\frac{y}{x}}} \]

   6. Applied egg-rr 30.7%

      \[\leadsto \color{blue}{\frac{y}{\frac{y}{x}}} \]
   7. Step-by-step derivation

      1. frac-2neg 30.7%

         \[\leadsto \color{blue}{\frac{-y}{-\frac{y}{x}}} \]

      2. div-inv 30.7%

         \[\leadsto \color{blue}{\left(-y\right) \cdot \frac{1}{-\frac{y}{x}}} \]

      3. distribute-neg-frac 30.7%

         \[\leadsto \left(-y\right) \cdot \frac{1}{\color{blue}{\frac{-y}{x}}} \]

   8. Applied egg-rr 30.7%

      \[\leadsto \color{blue}{\left(-y\right) \cdot \frac{1}{\frac{-y}{x}}} \]
   9. Step-by-step derivation

      1. un-div-inv 30.7%

         \[\leadsto \color{blue}{\frac{-y}{\frac{-y}{x}}} \]

      2. clear-num 30.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{-y}{x}}{-y}}} \]

      3. add-sqr-sqrt 0.0%

         \[\leadsto \frac{1}{\frac{\frac{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}}{x}}{-y}} \]

      4. sqrt-unprod 30.8%

         \[\leadsto \frac{1}{\frac{\frac{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}}{x}}{-y}} \]

      5. sqr-neg 30.8%

         \[\leadsto \frac{1}{\frac{\frac{\sqrt{\color{blue}{y \cdot y}}}{x}}{-y}} \]

      6. sqrt-unprod 30.1%

         \[\leadsto \frac{1}{\frac{\frac{\color{blue}{\sqrt{y} \cdot \sqrt{y}}}{x}}{-y}} \]

      7. add-sqr-sqrt 30.1%

         \[\leadsto \frac{1}{\frac{\frac{\color{blue}{y}}{x}}{-y}} \]

      8. add-sqr-sqrt 0.0%

         \[\leadsto \frac{1}{\frac{\frac{y}{x}}{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}}} \]

      9. sqrt-unprod 11.8%

         \[\leadsto \frac{1}{\frac{\frac{y}{x}}{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}}} \]

      10. sqr-neg 11.8%

          \[\leadsto \frac{1}{\frac{\frac{y}{x}}{\sqrt{\color{blue}{y \cdot y}}}} \]

      11. sqrt-unprod 30.7%

          \[\leadsto \frac{1}{\frac{\frac{y}{x}}{\color{blue}{\sqrt{y} \cdot \sqrt{y}}}} \]

      12. add-sqr-sqrt 30.7%

          \[\leadsto \frac{1}{\frac{\frac{y}{x}}{\color{blue}{y}}} \]

   10. Applied egg-rr 30.7%

       \[\leadsto \color{blue}{\frac{1}{\frac{\frac{y}{x}}{y}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.4:\\ \;\;\;\;x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{y}{x}}{y}}\\ \end{array} \]

Alternative 3: 57.7% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.0305:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{y}{x}}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 0.0305) x (/ 1.0 (/ (/ y x) y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 0.0305) {
		tmp = x;
	} else {
		tmp = 1.0 / ((y / x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 0.0305d0) then
        tmp = x
    else
        tmp = 1.0d0 / ((y / x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 0.0305) {
		tmp = x;
	} else {
		tmp = 1.0 / ((y / x) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 0.0305:
		tmp = x
	else:
		tmp = 1.0 / ((y / x) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 0.0305)
		tmp = x;
	else
		tmp = Float64(1.0 / Float64(Float64(y / x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 0.0305)
		tmp = x;
	else
		tmp = 1.0 / ((y / x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 0.0305], x, N[(1.0 / N[(N[(y / x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 0.030499999999999999

   1. Initial program 99.9%

      \[x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in y around 0 65.8%

      \[\leadsto \color{blue}{x} \]

   if 0.030499999999999999 < y

   1. Initial program 99.6%

      \[x \cdot \frac{\sin y}{y} \]
   2. Step-by-step derivation

      1. *-commutative 99.6%

         \[\leadsto \color{blue}{\frac{\sin y}{y} \cdot x} \]

      2. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{\sin y \cdot x}{y}} \]

      3. associate-*r/ 99.7%

         \[\leadsto \color{blue}{\sin y \cdot \frac{x}{y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\sin y \cdot \frac{x}{y}} \]

   4. Taylor expanded in y around 0 28.8%

      \[\leadsto \color{blue}{y} \cdot \frac{x}{y} \]
   5. Step-by-step derivation

      1. clear-num 30.5%

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{y}{x}}} \]

      2. un-div-inv 30.5%

         \[\leadsto \color{blue}{\frac{y}{\frac{y}{x}}} \]

   6. Applied egg-rr 30.5%

      \[\leadsto \color{blue}{\frac{y}{\frac{y}{x}}} \]
   7. Step-by-step derivation

      1. frac-2neg 30.5%

         \[\leadsto \color{blue}{\frac{-y}{-\frac{y}{x}}} \]

      2. div-inv 30.5%

         \[\leadsto \color{blue}{\left(-y\right) \cdot \frac{1}{-\frac{y}{x}}} \]

      3. distribute-neg-frac 30.5%

         \[\leadsto \left(-y\right) \cdot \frac{1}{\color{blue}{\frac{-y}{x}}} \]

   8. Applied egg-rr 30.5%

      \[\leadsto \color{blue}{\left(-y\right) \cdot \frac{1}{\frac{-y}{x}}} \]
   9. Step-by-step derivation

      1. un-div-inv 30.5%

         \[\leadsto \color{blue}{\frac{-y}{\frac{-y}{x}}} \]

      2. clear-num 30.5%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{-y}{x}}{-y}}} \]

      3. add-sqr-sqrt 0.0%

         \[\leadsto \frac{1}{\frac{\frac{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}}{x}}{-y}} \]

      4. sqrt-unprod 30.3%

         \[\leadsto \frac{1}{\frac{\frac{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}}{x}}{-y}} \]

      5. sqr-neg 30.3%

         \[\leadsto \frac{1}{\frac{\frac{\sqrt{\color{blue}{y \cdot y}}}{x}}{-y}} \]

      6. sqrt-unprod 29.6%

         \[\leadsto \frac{1}{\frac{\frac{\color{blue}{\sqrt{y} \cdot \sqrt{y}}}{x}}{-y}} \]

      7. add-sqr-sqrt 29.6%

         \[\leadsto \frac{1}{\frac{\frac{\color{blue}{y}}{x}}{-y}} \]

      8. add-sqr-sqrt 0.0%

         \[\leadsto \frac{1}{\frac{\frac{y}{x}}{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}}} \]

      9. sqrt-unprod 11.9%

         \[\leadsto \frac{1}{\frac{\frac{y}{x}}{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}}} \]

      10. sqr-neg 11.9%

          \[\leadsto \frac{1}{\frac{\frac{y}{x}}{\sqrt{\color{blue}{y \cdot y}}}} \]

      11. sqrt-unprod 30.5%

          \[\leadsto \frac{1}{\frac{\frac{y}{x}}{\color{blue}{\sqrt{y} \cdot \sqrt{y}}}} \]

      12. add-sqr-sqrt 30.5%

          \[\leadsto \frac{1}{\frac{\frac{y}{x}}{\color{blue}{y}}} \]

   10. Applied egg-rr 30.5%

       \[\leadsto \color{blue}{\frac{1}{\frac{\frac{y}{x}}{y}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 0.0305:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{y}{x}}{y}}\\ \end{array} \]

Alternative 4: 57.4% accurate, 14.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 6.5e-18) x (* y (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 6.5e-18) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 6.5d-18) then
        tmp = x
    else
        tmp = y * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 6.5e-18) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 6.5e-18:
		tmp = x
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 6.5e-18)
		tmp = x;
	else
		tmp = Float64(y * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 6.5e-18)
		tmp = x;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 6.5e-18], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.50000000000000008e-18

   1. Initial program 99.9%

      \[x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in y around 0 65.1%

      \[\leadsto \color{blue}{x} \]

   if 6.50000000000000008e-18 < y

   1. Initial program 99.6%

      \[x \cdot \frac{\sin y}{y} \]
   2. Step-by-step derivation

      1. *-commutative 99.6%

         \[\leadsto \color{blue}{\frac{\sin y}{y} \cdot x} \]

      2. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{\sin y \cdot x}{y}} \]

      3. associate-*r/ 99.8%

         \[\leadsto \color{blue}{\sin y \cdot \frac{x}{y}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\sin y \cdot \frac{x}{y}} \]

   4. Taylor expanded in y around 0 35.0%

      \[\leadsto \color{blue}{y} \cdot \frac{x}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]

Alternative 5: 57.7% accurate, 14.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 8000000.0) x (/ y (/ y x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 8000000.0) {
		tmp = x;
	} else {
		tmp = y / (y / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 8000000.0d0) then
        tmp = x
    else
        tmp = y / (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 8000000.0) {
		tmp = x;
	} else {
		tmp = y / (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 8000000.0:
		tmp = x
	else:
		tmp = y / (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 8000000.0)
		tmp = x;
	else
		tmp = Float64(y / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 8000000.0)
		tmp = x;
	else
		tmp = y / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 8000000.0], x, N[(y / N[(y / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8e6

   1. Initial program 99.9%

      \[x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in y around 0 65.3%

      \[\leadsto \color{blue}{x} \]

   if 8e6 < y

   1. Initial program 99.6%

      \[x \cdot \frac{\sin y}{y} \]
   2. Step-by-step derivation

      1. *-commutative 99.6%

         \[\leadsto \color{blue}{\frac{\sin y}{y} \cdot x} \]

      2. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{\sin y \cdot x}{y}} \]

      3. associate-*r/ 99.8%

         \[\leadsto \color{blue}{\sin y \cdot \frac{x}{y}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\sin y \cdot \frac{x}{y}} \]

   4. Taylor expanded in y around 0 29.3%

      \[\leadsto \color{blue}{y} \cdot \frac{x}{y} \]
   5. Step-by-step derivation

      1. clear-num 31.0%

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{y}{x}}} \]

      2. un-div-inv 31.0%

         \[\leadsto \color{blue}{\frac{y}{\frac{y}{x}}} \]

   6. Applied egg-rr 31.0%

      \[\leadsto \color{blue}{\frac{y}{\frac{y}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \end{array} \]

Alternative 6: 52.3% accurate, 105.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 x)

C

double code(double x, double y) {
	return x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x
end function

Java

public static double code(double x, double y) {
	return x;
}

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

function tmp = code(x, y)
	tmp = x;
end

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 99.8%

   \[x \cdot \frac{\sin y}{y} \]

2. Taylor expanded in y around 0 52.7%

   \[\leadsto \color{blue}{x} \]

3. Final simplification 52.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023279 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))